Sinusoidal wave formation for reduction of oscillations, harmonics and distortion using short pulses to reduce the number of required impedance injection units

1. A method for synchronized injection of impedance into high voltage (HV) transmission line, the method comprising: generating, by a plurality of impedance injection units (IIUs) coupled to the HV transmission line, impedance injection waves that cumulatively form a pseudo-sinusoidal wave, wherein the impedance injection waves comprise a first subgroup of one or more impedance injection waves and a second subgroup of one or more impedance injection waves; aligning and synchronizing, by the plurality of IIUs, the first and second subgroups of impedance injection waves with each other to reduce a step height of the pseudo-sinusoidal wave, the first subgroup of impedance injection waves each having an amplitude greater than an amplitude of each of the second subgroup of impedance injection waves; and injecting, by the plurality of IIUs, the pseudo-sinusoidal wave, as impedance, into the HV transmission line; wherein the plurality of IIUs form multiple connection configurations in sequence, each connection configuration comprising one IIU or multiple IIUs in series, parallel or combination thereof, coupled to the HV transmission line.

2. The method of claim 1 , wherein the pseudo-sinusoidal wave has a root-mean-squared (RMS) value or an average value about a RMS value or average value of a pure sinusoidal wave.

3. The method of claim 1 , wherein the first subgroup of impedance injection waves each having a duration greater than a duration of each of the second subgroup of impedance injection waves.

4. The method of claim 1 , wherein each of the impedance injection waves is generated at a start time=sin −1 {(2n−1)/2n} and a stop time=Π−sin −1 {(2n−1)/2n}, wherein n is a step in the pseudo-sinusoidal wave.

5. The method of claim 1 , wherein an ideality factor of the pseudo-sinusoidal wave is about an average value of a pure sinusoidal wave.

6. The method of claim 1 , wherein the amplitude of the second subgroup of impedance injection waves is half of the amplitude of the first subgroup of impedance injection waves.

7. The method of claim 1 , wherein the plurality of IIUs comprise a first subgroup of IIUs that generates the first subgroup of impedance injection waves, and a second subgroup of IIUs that generates the second subgroup of impedance injection waves.

8. The method of claim 1 , wherein aligning and synchronizing the first and second subgroups of impedance injection waves with each other comprises aligning each impedance injection wave of the second subgroup of impedance injection waves on a left side or a right side of an impedance injection wave of the first subgroup of impedance injection waves.

9. The method of claim 1 , wherein the pseudo-sinusoidal wave reduces generation of oscillations, harmonics and distortion on the HV transmission line, as compared to injection of a single impedance injection wave.

10. A system for injecting impedance into a high voltage (HV) transmission line, the system comprising: a plurality of impedance injection units (IIUs) coupled to the HV transmission line, the plurality of IIUs forming multiple connection configurations in sequence, each connection configuration comprising one IIU or multiple IIUs in series, parallel or combination thereof, coupled to the HV transmission line; wherein the plurality of impedance injection units (IIUs) are to: generate impedance injection waves that cumulatively form a pseudo-sinusoidal wave, wherein the impedance injection waves comprise a first subgroup of one or more impedance injection waves and a second subgroup of one or more impedance injection waves, align and synchronize the first and second subgroups of impedance injection waves with each other to reduce a step height of the pseudo-sinusoidal wave, the first subgroup of impedance injection waves each having an amplitude greater than an amplitude of each of the second subgroup of impedance injection waves, and inject the pseudo-sinusoidal wave, as impedance, into the HV transmission line.

11. The system of claim 10 , wherein the pseudo-sinusoidal wave has a root-mean-squared (RMS) value or an average value about a RMS value or average value of the pure sinusoidal wave.

12. The system of claim 10 , wherein the first subgroup of impedance injection waves each having a duration greater than a duration of each of the second subgroup of impedance injection waves.

13. The system of claim 10 , wherein each of the impedance injection waves is generated at a start time=sin −1 {(2n−1)/2n} and a stop time=Π−sin −1 {(2n−1)/2n}, wherein n is a step in the pseudo-sinusoidal wave.

14. The system of claim 10 , wherein an ideality factor of the pseudo-sinusoidal wave is about an average value of a pure sinusoidal wave.

15. The system of claim 10 , wherein the amplitude of the second subgroup of impedance injection waves is half of the amplitude of the first subgroup of impedance injection waves.

16. The system of claim 10 , wherein the plurality of IIUs comprise a first subgroup of IIUs that generates the first subgroup of impedance injection waves, and a second subgroup of IIUs that generates the second subgroup of impedance injection waves.

17. The system of claim 10 , wherein to align and synchronize the first and second subgroups of impedance injection waves with each other, the plurality of IIUs align each impedance injection wave of the second subgroup of impedance injection waves on a left side or a right side of an impedance injection wave of the first subgroup of impedance injection waves.

18. The system of claim 10 , wherein the pseudo-sinusoidal wave reduces generation of oscillations, harmonics and distortion on the HV transmission line, as compared to injection of a single impedance injection wave.